Kategoria BISAC: Mathematics >> Differential Equations - General

An outgrowth of The Seventh International Conference on Integral Methods in Science and Engineering, this book focuses on applications of integration-based analytic and numerical techniques. The contributors to the volume draw from a number of physical domains and propose diverse treatments for various mathematical models through the use of integration as an essential solution tool.

Physically meaningful problems in areas related to finite and boundary element techniques, conservation laws, hybrid approaches, ordinary and partial differential equations, and vortex methods...

First posed by Hermann Weyl in 1910, the limit point/limit circle problem has inspired, over the last century, several new developments in the asymptotic analysis of nonlinear differential equations. This monograph traces the evolution of this problem from its inception to its modern-day extensions to the study of deficiency indices and analogous properties for nonlinear equations.

The book opens with a discussion of the problem in the linear case, as Weyl originally stated it, and then proceeds to a generalization for nonlinear higher-order equations. En route, the authors...

Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica(R) provides a general framework useful for the applications on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica(R) software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use of ODEs and Mathematica(R) in the dynamics of rigid bodies.

Mathematical methods and scientific computation are...

This text features a careful treatment of flow lines and algebraic invariants in contact form geometry, a vast area of research connected to symplectic field theory, pseudo-holomorphic curves, and Gromov-Witten invariants (contact homology). In particular, it develops a novel algebraic tool in this field: rooted in the concept of critical points at infinity, the new algebraic invariants defined here are useful in the investigation of contact structures and Reeb vector fields. The book opens with a review of prior results and then proceeds through an examination of variational problems,...